Stability of peakons for the Degasperis-Procesi equation
نویسندگان
چکیده
The Degasperis-Procesi equation can be derived as a member of a oneparameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the CamassaHolm equation. It is noted that the Degasperis-Procesi equation, unlike the Camassa-Holm equation, has not only peakon solitons but also shock peakons. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis-Procesi equation on the line. By constructing a Liapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations.
منابع مشابه
Integrable and non-integrable equations with peakons
We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new integrable equation first isolated by Degasperis and Procesi. A Lagrangian and Hamiltonian formulation is presented for the whole family of equations, and we discuss how this fits into a bi-Hamiltonian framework in the integrable cases. The Hamilton...
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